The Schur ℓ1 Theorem for Filters

  • Antonio Aviles Lopez Equipe de Logique Mathématique UFR de Mathématiques (case 7012), Université Denis-Diderot Paris, 72 place Jussieu, 75251 Paris Cedex 05, France
  • Bernardo Cascales Salinas Departamento de Matemсticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
  • Vladimir Kadets Department of Mathematics and Mechanics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine
  • Alexander Leonov Department of Mathematics and Mechanics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine

Анотація

We study the classes of filters ℱ on ℕ such that the weak and strong ℱ-convergence of sequences in ℓ1 coincide. We study also an analogue of ℓ1 weak sequential completeness theorem for filter convergence.

Mathematics Subject Classification: 46B25, 54A20.

Ключові слова:

Schur ℓ1 theorem, weak sequential completeness, filter convergence, filter, statistical convergence.

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Як цитувати

(1)
A. A. Lopez, B. C. Salinas, V. Kadets, A. Leonov, The Schur ℓ1 Theorem for Filters, Журн. мат. фіз. анал. геом. 3 (2007), 383-398.

Номер

Том 3 № 4 (2007)

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